Stability Analysis and Numerical Simulation of a Car-Following Model Considering Safety Potential Field and V2X Communication: A Focus on Influence Weight of Multiple Vehicles

In a V2X environment, the target vehicle is capable of acquiring motion information from multiple vehicles ahead, and this information plays a crucial role in predicting the target vehicle's motion behavior. To better understand how leading vehicles affect the car-following behavior of the target vehicle, we have developed an improved car-following model that considers the effects of multiple leading vehicles. This model constructs distance-based and field-based models to describe the influence weights of different vehicles on the target vehicle. The stability conditions of the model were obtained through linear stability analysis, and the mKdV equation, which describes the evolution characteristics of traffic density waves in congested areas, was determined through nonlinear analysis. Numerical simulations were conducted to discuss the multi-vehicle effect λ, different vehicle influence weights (distance-based and field-based models) βj, and the number of leading vehicles considered q. The study found that in congested areas, initial perturbations evolve in the form of kink-antikink waves, moving rearward, with the amplitude of the headway curve decreasing as the multi-vehicle effect coefficient value increases. For different vehicle influence weights, the field-based model outperforms the distance-based model. Moreover, as the number of leading vehicles considered q increases, the stability of traffic flow gradually improves. The numerical results are consistent with the theoretical findings, and it is noted that the model successfully enhances vehicular movement efficiency, reduces congestion, and improves road safety. To minimize collision incidents, the improved model can be implemented as an active safety technology.